A leaf shutter enables high flash synch speeds. This means that you can use the combination of fast shutter speed and large aperture to balance ambient light and fill flash, even in the brightest sunlight. That combination of settings made the image below possible. Let's put it this way: if the camera did an auto exposure of the image below, the sky would be correctly exposed, and the leaves would be quite dark. I used flash to expose the leaves, and a fast shutter speed to underexpose the sky, which darkened it and also made the blue more vibrant.

Fuji X100T 23mm f21/4000 @ f4.0with flash set to overexpose, I forget by how much.